Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class karenAndGame {
	public static void main(String[] args) {
		FastScanner scan=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		int n=scan.nextInt(), m=scan.nextInt();
		int[][] a=new int[n][m];
		int min=Integer.MAX_VALUE;
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=scan.nextInt();
				min=Math.min(min,a[i][j]);
			}
		}
		ArrayList<String> res=new ArrayList<>();
		int r=Math.min(n,m);
		String s="";
		if(r==n) s="row ";
		else s="col ";
		for(int i=0;i<min;i++) {
			for(int j=1;j<=r;j++) {
				res.add(s+j);
			}
		}
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]-=min;
			}
		}
		boolean[][] v=new boolean[n][m];
		
		ArrayDeque<Integer> q=new ArrayDeque<>();
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				if(a[i][j]==0) {
					q.offer(i);
					q.offer(j);
					v[i][j]=true;
				}
			}
		}
		while(!q.isEmpty()) {
			//if there is a nonzero element in the same row as this one
			//it must be taken care of by columns
			//and vice versa
			
			int ci=q.poll(), cj=q.poll();
//			System.out.println("at+ "+ci+" "+cj);
			for(int i=0;i<n;i++) {
				if(a[i][cj]!=0) {
					int mi=Integer.MAX_VALUE;
					for(int j=0;j<m;j++) {
//						System.out.println(i+" "+j);
						mi=Math.min(mi,a[i][j]);
					}
					if(mi<a[i][cj]) {
						out.println(-1);
						out.close();
						return;
					}
					for(int j=0;j<m;j++) {
//						System.out.println(i+" sub "+j);
						a[i][j]-=mi;
						if(a[i][j]==0&&!v[i][j]) {
							q.offer(i);
							q.offer(j);
							v[i][j]=true;
						}
					}
//					for(int[] aa:a) System.out.println(Arrays.toString(aa));
					for(int k=0;k<mi;k++) res.add("row "+(i+1));
				}
			}
			for(int j=0;j<m;j++) {
				if(a[ci][j]!=0) {
					int mi=Integer.MAX_VALUE;
					for(int i=0;i<n;i++) {
//						System.out.println(i+" "+j+" "+a[i][j]);
						mi=Math.min(mi,a[i][j]);
					}
					if(mi<a[ci][j]) {
						out.println(-1);
						out.close();
						return;
					}
					for(int i=0;i<n;i++) {
//						System.out.println(i+" sub "+j);
						a[i][j]-=mi;
						if(a[i][j]==0&&!v[i][j]) {
							q.offer(i);
							q.offer(j);
							v[i][j]=true;
						}
					}
//					for(int[] aa:a) System.out.println(Arrays.toString(aa));
					for(int k=0;k<mi;k++) res.add("col "+(j+1));
				}
			}
//			for(int[] aa:a) System.out.println(Arrays.toString(aa));
		}
		boolean good=true;
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				good&=v[i][j];
			}
		}
		if(!good) out.println(-1);
		else {
			out.println(res.size());
			for(String x:res) out.println(x);
		}
		out.close();
		return;
	}
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			try	{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e){e.printStackTrace();}
		}

		public String next() {
			if (st.hasMoreTokens())	return st.nextToken();
			try {st = new StringTokenizer(br.readLine());}
			catch (Exception e) {e.printStackTrace();}
			return st.nextToken();
		}

		public int nextInt() {return Integer.parseInt(next());}

		public long nextLong() {return Long.parseLong(next());}

		public double nextDouble() {return Double.parseDouble(next());}

		public String nextLine() {
			String line = "";
			if(st.hasMoreTokens()) line = st.nextToken();
			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
			while(st.hasMoreTokens()) line += " "+st.nextToken();
			return line;
		}
	}
}